Let $\bf{A}$ be a $n\times n$ matrix, $\bf{b}$ be $p-$vector, and $\bf{x}$ be $p-$vector. Compute $$\frac{\partial^2Q(\bf{x})}{\partial\bf{x}\partial\bf{x^T}}$$ where $Q\bf{(x)=(b-Ax)^T(b-Ax)}$.
Textbook Solution: $Q\bf{(x)=(b-Ax)^T(b-Ax)}\\\qquad \;= \bf{b^Tb-2x^TA^Tb+x^TA^TAx}.$
Hence, $\dfrac{\partial Q(\bf{x})}{\partial\bf{x}}=\bf{2A^Tb+2A^TAx}$
Thus, $\dfrac{\partial^2Q(\bf{x})}{\partial\bf{x}\partial\bf{x^T}}=2\bf{A^TA}.$
My Solution: $Q\bf{(x)=b^Tb-2x^TA^Tb+x^TA^TAx}$
Hence, $\dfrac{\partial Q(\bf{x})}{\partial\bf{x}}=\bf{-2A^Tb+A^TAx}$
Thus, $\dfrac{\partial^2Q(\bf{x})}{\partial\bf{x}\partial\bf{x^T}}=\bf{A^TA}$
Question: Did I made any mistake? And if not why is my answer not matching?